Author: Harvey Cao

Qubit efficient quantum algorithms for the vehicle routing problem on quantum computers of the NISQ era
Ioannis D. Leonidas, Alexander Dukakis, Benjamin Tan, Dimitris G. Angelakis
arXiv:2306.08507

The vehicle routing problem with time windows (VRPTW) is a classic optimization problem that arises in many different areas, such as logistics and transportation. The goal of the VRPTW is to find the shortest possible route for a fleet of vehicles to visit a set of destinations. In recent years, there has been growing interest in using variational quantum algorithms (VQAs), to find approximate solutions to problems that can be formulated as quadratic unconstrained binary optimization (QUBO) problems. In this work, we formulate the VRPTW as a QUBO and apply a quantum variational approach to the VRPTW using our earlier suggested encoding scheme described in [1] to reduce drastically the number of qubits required. We evaluate our approach on a set of VRPTW instances ranging from 11 to 3964 routes constructed with data provided by researchers from ExxonMobil. We compare the solutions obtained with standard full encoding approaches for which the max problems size possible in NISQ era are of the order of 20-30 routes. We run our algorithms in simulators as well as cloud quantum hardware provided by IBMQ, AWS (Rigetti) and IonQ and benchmark our results against each other as well as on the simulators. We show that our approach can find approximate solutions to the VRPTW that are comparable to the solutions found by quantum algorithms using the full encoding. Our results suggest that our unique encoding approach, provides a promising approach to drastically reducing the number of qubits required to find decent approximate solutions for industry-based optimization problems.

Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer
Chong Hian Chee, Daniel Leykam, Adrian M. Mak, Dimitris G. Angelakis
C. H. Chee et al., Phys. Rev. A 108, 022416 (2023)

Preparing quantum ansatzes is a necessary prerequisite in many quantum algorithms for quantum chemistry such as the variational quantum eigensolver. Widely-used ansatzes including the Slater determinants and Unitary Coupled Cluster, employ parameterized fermionic excitation gates, with the latter resulting in deep quantum circuits that scale at least polynomially with the system size N. Here we propose an alternate paradigm for fermionic ansatz state preparation inspired by data-loading circuits methods developed for quantum machine learning. Our approach provides a shallower, yet scalable O(dlog2^N) two-qubit gate depth preparation of d-fermion Slater determinants and correlated states, a subexponential improvement in gate depth over existing approaches. This is particularly important as it can be implemented on planar architectures without qubit swapping overheads, thereby enabling the use of larger basis sets needed for high-precision quantum chemistry studies on near-term quantum devices.

Efficiently Extracting Multi-Point Correlations of a Floquet Thermalized System
Yong-Guang Zheng, Wei-Yong Zhang, Ying-Chao Shen, An Luo, Ying Liu, Ming-Gen He, Hao-Ran Zhang, Wan Lin, Han-Yi Wang, Zi-Hang Zhu, Ming-Cheng Chen, Chao-Yang Lu, Supanut Thanasilp, Dimitris G. Angelakis, Zhen-Sheng Yuan, Jian-Wei Pan
arXiv:2210.08556

Nonequilibrium dynamics of many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. It is proposed to be classically intractable to sample driven thermalized many-body states of Bose-Hubbard systems, and further extract multi-point correlations for characterizing quantum phases. Here, leveraging dedicated precise manipulations and number-resolved detection through a quantum gas microscope, we implement and sample a 32-site driven Hubbard chain in the thermalized phase. Multi-point correlations of up to 14th-order extracted from experimental samples offer clear distinctions between the thermalized and many-body-localized phases. In terms of estimated computational powers, the quantum simulator is comparable to the fastest supercomputer with currently known best algorithms. Our work paves the way towards practical quantum advantage in simulating Floquet dynamics of many-body systems.

Computing Electronic Correlation Energies using Linear Depth Quantum Circuits
Chong Hian Chee, Adrian M. Mak, Daniel Leykam, Panagiotis Kl Barkoutsos, Dimitris G. Angelakis
C. H. Chee et al., Quantum Sci. Technol. 9, 025003 (2024)

Efficient computation of molecular energies is an exciting application of quantum computers, but current noisy intermediate-scale quantum (NISQ) devices can only execute shallow circuits, limiting existing quantum algorithms to small molecules. Here we demonstrate a variational NISQ-friendly algorithm for computing electronic correlation energies perturbatively, trading deep circuits in exchange for more shallow circuits with depth linear in the number of qubits. We tested the algorithm on several small molecules, both with classical simulations including noise models and on cloud quantum processors, showing that it not only reproduces the equilibrium molecular energies but it also captures the perturbative electronic correlation effects at longer bond distances. As fidelities of quantum processors continue to improve our algorithm will enable the study of larger molecules compared to existing approaches with higher-order polynomial circuit depth.

Topological data analysis and machine learning
Daniel Leykam, Dimitris G. Angelakis
arXiv:2206.15075

Topological data analysis refers to approaches for systematically and reliably computing abstract “shapes” of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest among physicists. We present a concise yet (we hope) comprehensive review of applications of topological data analysis to physics and machine learning problems in physics including the detection of phase transitions. We finish with a preview of anticipated directions for future research.

Fock State-enhanced Expressivity of Quantum Machine Learning Models
Beng Yee Gan, Daniel Leykam, Dimitris G. Angelakis
EPJ Quantum Technology 9 (1), 16

The data-embedding process is one of the bottlenecks of quantum machine learning, potentially negating any quantum speedups. In light of this, more effective data-encoding strategies are necessary. We propose a photonic-based bosonic data-encoding scheme that embeds classical data points using fewer encoding layers and circumventing the need for nonlinear optical components by mapping the data points into the high-dimensional Fock space. The expressive power of the circuit can be controlled via the number of input photons. Our work shed some light on the unique advantages offers by quantum photonics on the expressive power of quantum machine learning models. By leveraging the photon-number dependent expressive power, we propose three different noisy intermediate-scale quantum-compatible binary classification methods with different scaling of required resources suitable for different supervised classification tasks.